1.28 shows the response of a mated pair of 1 mm male‐to‐male and female‐to‐female adapters (right scale) along with the same 1.85 mm mated pair of Figure 1.27 (left scale). The reference line is offset by 1 division to make it easier to see the traces; without the offset, the traces would lie nearly on top of each other. The mode for 1 mm is a bit of a deeper mode but is now out past 120 GHz. There is a second mode at 124 GHz, but both are also non‐propagating, so it may be possible to remove them with calibration. The depth of the mode does imply that it may be from the multiple beads in the mated pair and not be very stable with changes in temperature.
Figure 1.28 Response of a 1 mm mated pair and a 1.85 mm mated pair.
1.8.2.9 PC Board Launches and Cable Connectors
For many design and measurement applications, the circuit of interest is embedded in a PC board. There are many types and styles of PC board launches, which typically have an SMA connector on one end and PC board contacts at the other, as well as miniature versions such as the QMA connector. These can come in edge launch as well as right angle, and their performance depends greatly upon the mounting pattern on the PC board trace. These can be difficult to characterize because only one end is available in a standard connector. An example of a common PC board launch is shown in Figure 1.29. Measurement techniques for these devices, as well as methods to remove their effects from the measurement of on‐board PC components, are discussed in Chapter 11.
Figure 1.29 PC board SMC launches.
Connectors designed for coaxial‐cables provide similar challenges, as the cable to which they are attached affects the quality of the connection, and the common practice of attaching two connectors to each end of cable makes it difficult to separate the effects of one from the other. Time‐domain techniques can be applied to remove these unwanted effects, as described in Chapter 5.
1.8.3 Non‐coaxial Transmission Lines
Transmission lines provide the interconnection between components, typically in a microcircuit or a PC board. These are distinguished from a measurement perspective because they are typically much shorter, often not shielded, and the interface to them is not easy to make and sometimes not well defined. While there have been whole books written on the subject, a short review of some common transmission line structures and their attributes are described next, with a focus on attributes important to measurement. Transmission lines are characterized by the same three parameters: impedance, effective dielectric constant, and loss.
1.8.3.1 Microstrip
Certainly the most widespread transmission line must be the microstrip line, shown in Figure 1.30. This is found in planar structures such as PC boards and micro‐circuits. Consisting of a thin strip of metal on a dielectric substrate, over a ground plane, it is used for connection between components as well as creating transmission line components such as couplers and filters (Hong and Lancaster 2001).
Figure 1.30 Planer transmission lines: microstrip (a), coplanar waveguide (b), strip line (c).
The computation of the transmission parameters has been fully documented in many forms, but for measurement purposes these lines are typically 50 Ω (or the equivalent system impedance) even though as a design element they can take on any value. For most applications, the dielectric constant is 10 or less, so the w/h ratio is greater than 1 for 50 Ω. The approximate impedance can be computed as (Pozar 1990)
(1.86)
where εre is the effective relative‐dielectric‐constant, found from
(1.87)
The effective relative‐dielectric constant sets the velocity factor of the transmission line, but in microstrip, some of the fields travel in the substrate and some in air. Therefore, the transmission is not purely transverse‐electromagnetic (TEM), and some structures become more difficult to design, particularly coupled lines, the even and odd mode velocity factors of which are not the equal. Since the line is not pure TEM, at high frequency, dispersion effects will become apparent where the effective delay of the line is not constant with frequency.
The loss of microstrip lines is difficult to compute accurately because it depends upon many factors including the conductivity of the microstrip line and the ground plan, the dielectric loss of the substrate, radiated loss to the housing or shield, and losses related to both surface roughness and edge roughness. These roughness losses can be significant in PC board and low‐temperature cofired‐ceramic (LTCC) applications and are dependent upon the particular processes used. While there are high‐quality PC board materials (Duriod™ or GTEK™ are common trade names), the material known as FR4 is most common, and the dielectric constant and loss of this PC board material can be uncertain. The finished substrate can be comprised of layers of board material sandwiched together with glue, and the final thickness can depend upon processing steps, so it is best when evaluating microstrip transmission lines to produce sample structures that can help determine the exact nature of the material.
One high‐performance material used is single‐crystal sapphire, and it has the unusual property of having a dielectric constant that has a directionality, with a higher constant of 10.4 in one of the three dimensions, and a lower constant of 9.8 in the other two. A second, common high‐performance dielectric is ceramic found in thin‐film, thick‐film, and LTCC applications. It has a uniform dielectric constant typically between 9.6 and 9.8 depending upon the purity and grain structure of the ceramic.
1.8.3.2 Other Quasi‐Microstrip Structures
For many applications, the size of 50 Ω microstrip line is not suitable for connections to very large devices. Some common modifications are suspended substrate microstrip line, where the ground plan has been removed some distance from the dielectric. This has the effect of lowering the effective dielectric constant and raising the impedance of the line. In this way, a wider line can be used to connect to a wide component and still maintain a matched impedance. A shielded microstrip line is entirely enclosed (the theoretical models of microstrip lines assume no top shield), and the top metal tends to lower the impedance of the line. This is particularly true for suspended microstrip lines.
1.8.3.3 Coplaner Waveguide
One
